Question

Let $a,\lambda ,\mu \in R.$ Consider the system of linear equations $ax+2y=\lambda $ and $3x-2y=\mu .$ Which of the following statement is INCORRECT?

• A. If $a=-3,$ then the system has infinitely many solutions for all values of $\lambda $ and $\mu $
• B. If $a\neq -3,$ then the system has a unique solution for all values of $\lambda $ and $\mu $
• C. If $\lambda +\mu =0,$ then the system has infinitely many solutions for $a=-3$
• D. If $\lambda +\mu \neq 0,$ then the system has no solution for $a=-3$

Answer 1

Answer: (A)

$ax+2y=\lambda $
$3x-2y=\mu $
For $a=-3,$ above lines will be parallel or coincident
Also parallel for $\lambda +\mu \neq 0$ and coincident $\lambda +\mu =0$
and if $a\neq -3,$ lines are intersecting $\Rightarrow $ unique solution.